How do we figure the odds of making this runner/runner draw

[Carmine]

Hero holds AA
Opponent holds T8

Flop: 79J

On the turn I need to hit and Ace or have the board pair then I need the other outcome on the river (IE if and Ace hits the turn I need another ace on river or board to pair. If board pairs on the turn I need to hit same paired card to hit river or an ace.)

It gets confusing for me because the number of outs change depending on which event occurs first.

[BruceZ]

[ QUOTE ]
Hero holds AA
Opponent holds T8

Flop: 79J

On the turn I need to hit and Ace or have the board pair then I need the other outcome on the river (IE if and Ace hits the turn I need another ace on river or board to pair. If board pairs on the turn I need to hit same paired card to hit river or an ace.)

It gets confusing for me because the number of outs change depending on which event occurs first.

[/ QUOTE ]

It's easiest to think of the 2-card combinations you need, and the number of ways to make each one. They are:

A7 (2*3 = 6)
A9 (2*3 = 6)
AJ (2*3 = 6)
AA (1)
77 (3)
99 (3)
JJ (3)
========
total = 28

Total possible 2-card combinations with 45 cards remaining is C(45,2) = 45*44/2 = 990, and 27/990 =~ 2.8%. Since 990 is close to 1000, you can get an accurate result in your head just by counting the hands and moving the decimal point. Note that there are also 9 hands that tie (T8).